DCM Conjoint Additive Kernel

> Conjoint Method Overview > DCM Conjoint Additive Kernel

Behavioral model

In common practice of conjoint method, utility of a product is made up as a sum of part-worths of individual attribute levels (main effects) and, possibly, their interactions. This additive property of the conjoint method kernel is known as "compositional rule". Utilities computed this way are viewed as parameters of the link to distribution function of the modeled behavior. If the behavioral model is multinomial, the resulting overall model is known as multinomial logit model [Luce, 1958; McFadden, 1974]. Non-linear links are applied in some hierarchical models of behavior, e.g. multiplicative link in the nested "mother logit" model (preference tree [Tversky and Sattah, 1979], multi-level decision choice) or multi-latent-class based disaggregated models.

As aside

Due to complexity of the problem, a multi-level hierarchical approach in modeling is limited mostly to academic or generously sponsored studies.

The main consequence of the additivity in linear models is obvious. A change in value of a kernel constituent (a part-worth) can be compensated with a change of another constituent in the other direction. This may not be always true. For example, if a product is unaffordable, no change in any of the attributes except the price can make the product acceptable. An unbiased estimation of valid additive kernel constituents requires to meet at least the following conditions (see more in profile properties):

The view of a product composed from attributes (synthesis):
- Levels of an attribute should be allowed to be set independently from levels of all other attributes.
- All allowed level combinations must be managerially reasonable.
The view of a product decomposed to attributes (analysis):
- If the attributes are mutually independent in their influence on the product preference, only their main effects are needed to be considered.
- If there are significant behavioral interaction effects between attributes, the interactions must be included and the related parameters estimated.

From the view of conjoint exercise design, it is often unrealistic to combine all attribute levels freely, e.g. performance (quality) and price. A solution may be a blocked design composed of product classes.

In order to decrease the load on respondents and to increase discrimination efficiency of the interviewing it is useful to present a respondent only product profiles from or at least close to their consideration scope. The CBS - Choice Based Sampling may be used.

From the view of interpretation, individual-based utility estimates are, in general, preferred to aggregated (segment-based) ones. Preferences of individual consumers have variability that can hardly ever be explained by exogenous segment indicators.

Estimation of all possible individual-based interactions among levels is usually unfeasible due to an insufficient amount of the collected data. In some cases, a narrowing down the span of the attributes involved in the interactions is sufficient since the influence of interactions is usually much lower than that of main effects. If this is not applicable directly the approach of product classes may be a solution. As a matter of fact, the most frequent reason for the "observed" interactions is a deficient formulation of the attribute properties or models.

As aside

Extensions of the basic logit model such as linear nested models, mixed logit models or CEA - Cross Effect Analysis do not step out from the frame of the additive kernel assumptions. The same is true for some new attempts such as choice models based on the Random Regret Minimization (RRM) framework. The additive kernel model is the essence of the current state of the art.

Microeconomic models

In market research (MR), the purpose of all the effort to estimate behavioral model parameters is to predict the market events of interest in some quantitative units of consumption. Neo-classical econometric models of demand are, in essence, based on the notion of utility, price, income, supply, etc., mediated through a hypothesized utility maximization by individuals given certain constraints. In an aggregated market view, the constraints are usually derived from the income distribution. In an individual consumer view and within a quite restricted category of goods considered in a research study, the income distribution can be replaced by a hypothetical value of willingness to spend.

Two simple utility models of individual behavior of concern in conjoint studies are CES - Constant Elasticity of Substitution and CDES - Constant Differential Elasticity of Substitution. Both describe the whole spectrum of substitutability among goods.

The case of perfect complements obtains as zero elasticity of substitution. The MBC - Menu Based Choice type of interviewing sometimes reveals properties close to that in bundling and packaging problems.
The case of perfect substitutes obtains as infinite elasticity. This is an unattainable property in practice. Elasticity of substitution determined experimentally is seldom higher than 10.
Cobb-Douglas model is a special case of the CES preferences with elasticity of substitution equal to 1. This value is the minimum for substitutable goods.

The utility maximization constrained by the upper limit of willingness to spend ("income" in the traditional models) leads to individual demand models that can be compared to the multinomial logit model used in most conjoint analysis packages and share-based "market" simulators. In practice, additional constraints must be respected in the demand model for an individual.

Non-budget constraints

More does not always mean better in the real life decisions. The following saturation factors are of concern.

Physiological constraints:
- The amount of possibly consumed goods is finite.
- The time devoted to an activity is finite.
Psychological constraints:
- Contentment is achieved at gratification of needs at some utility level. This is equivalent to cost minimization rather than utility maximization.
- Satisfaction may come from resigning on gratification of needs. This often happens along with the perspective of using the saved expenses for an outer product with a potentially higher level of satisfaction.
- The product may not reach some level of availability, trustworthiness or convenience. There may be a threshold under which the event of interest will not proceed at all.
- Consumer is risk aversive. A higher benefit may well be perceived as a danger or inconvenience (e.g. increased expenses in the future).

An introduction of the above constraints may lead to models of demand substantially different from CES or CDES models. For some concurrent combinations of constraints there is no explicit solution. It is a task for the researcher how to involve the assumed constraints in the model and what approximations to adopt. Rather than to build a constrained model for a product as a fully specified object it is easier to apply constraints only to the affected attributes, e.g. as described in Attribute Properties and Models.